cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A038130 Beatty sequence for 2*Pi.

Original entry on oeis.org

0, 6, 12, 18, 25, 31, 37, 43, 50, 56, 62, 69, 75, 81, 87, 94, 100, 106, 113, 119, 125, 131, 138, 144, 150, 157, 163, 169, 175, 182, 188, 194, 201, 207, 213, 219, 226, 232, 238, 245, 251, 257, 263, 270, 276, 282, 289, 295, 301, 307, 314, 320, 326, 333, 339, 345
Offset: 0

Views

Author

Felice Russo

Keywords

Comments

a(n) = floor[circumference of a circle of radius n]. - Mohammad K. Azarian, Feb 29 2008
This sequence consists of the nonnegative integers k satisfying sin(k) <= 0 and sin(k+1) >= 0; thus this sequence and A246388 partition A022844 (the Beatty sequence for Pi). - Clark Kimberling, Aug 24 2014

Links

Crossrefs

Complement of A108586.
For ceiling (2*Pi*n) see A004082.
Cf. A022844, A140758, A108592, A246388.

Programs

  • Mathematica
    Table[Floor[2 n*Pi], {n, 0, 100}] (* or *)
Select[Range[0, 628], Sin[#] <= 0 && Sin[# + 1] >= 0 &] (* Clark Kimberling, Aug 24 2014 *)

Formula

a(n) = floor(2*Pi*n).
a(n) = A004082(n+1) - 1. - John W. Nicholson, Mar 20 2025

Extensions

More terms from Mohammad K. Azarian, Feb 29 2008

A108591 Self-inverse integer permutation induced by Beatty sequences for Pi and Pi/(Pi-1).

Original entry on oeis.org

3, 6, 1, 9, 12, 2, 15, 18, 4, 21, 25, 5, 28, 31, 7, 34, 37, 8, 40, 43, 10, 47, 50, 53, 11, 56, 59, 13, 62, 65, 14, 69, 72, 16, 75, 78, 17, 81, 84, 19, 87, 91, 20, 94, 97, 100, 22, 103, 106, 23, 109, 113, 24, 116, 119, 26, 122, 125, 27, 128, 131, 29, 135, 138, 30, 141, 144
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 11 2005

Keywords

Links

Crossrefs

Cf. A108590, A108592, A108599.

Formula

a(A022844(n))=A054386(n) and a(A054386(n))=A022844(n).

Extensions

a(53)/a(54) joined by Georg Fischer, May 24 2022

A108586 Floor(2*n*Pi/(2*Pi-1)).

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 82, 83, 84, 85
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 11 2005

Keywords

Comments

Beatty sequence for 2*Pi/(2*Pi-1); complement of A038130; not the same as A108120: a(37)=44 <> A108120(37)=43.

Links

Crossrefs

Cf. A054386, A140758, A108592.

Programs

  • Mathematica
    With[{c=2Pi},Floor[(c*Range[80])/(c-1)]] (* Harvey P. Dale, Apr 21 2024 *)

A108590 Self-inverse integer permutation induced by Beatty sequences for Pi/2 and Pi/(Pi-2).

Original entry on oeis.org

2, 1, 5, 8, 3, 11, 13, 4, 16, 19, 6, 22, 7, 24, 27, 9, 30, 33, 10, 35, 38, 12, 41, 14, 44, 46, 15, 49, 52, 17, 55, 57, 18, 60, 20, 63, 66, 21, 68, 71, 23, 74, 77, 25, 79, 26, 82, 85, 28, 88, 90, 29, 93, 96, 31, 99, 32, 101, 104, 34, 107, 110, 36, 112, 115, 37, 118, 39, 121
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 11 2005

Keywords

Links

Crossrefs

Cf. A108591, A108592.

Formula

a(A140758(n))=A108589(n) and a(A108589(n))=A140758(n).

A108593 Self-inverse integer permutation induced by Beatty sequences for 1/sin(1) and 1/(1-sin(1)).

Original entry on oeis.org

6, 12, 18, 25, 31, 1, 37, 44, 50, 56, 63, 2, 69, 75, 82, 88, 94, 3, 100, 107, 113, 119, 126, 132, 4, 138, 145, 151, 157, 164, 5, 170, 176, 182, 189, 195, 7, 201, 208, 214, 220, 227, 233, 8, 239, 246, 252, 258, 264, 9, 271, 277, 283, 290, 296, 10, 302, 309, 315, 321
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 11 2005

Keywords

Links

Crossrefs

Cf. A108592.

Formula

a(A108120(n))=A108587(n) and a(A108587(n))=A108120(n).
Showing 1-5 of 5 results.

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